Problemas de escalamiento en el modelaje de rocas sedimentarias y sus posibles soluciones por medio del uso de geometrías fractales

Abstract:

The pore space affects for most of the physical processes that we observe in sedimentary rocks. In particular, it affects the behavior of the elastic modules of the material drastically. To explain the elastic behavior of porous rocks, theoretical models have been proposed whose analytic solutions describe the deformations of the pores in function of applied stresses. However, these models only consider solutions for simple porous geometries, because it is very difficult to obtain exact solutions for models with complex geometries. The topologies of the porous spaces observed in real rocks are quite complex, due to the processes of natural formation that originated the rocks. This fact indicates that realistic models should contain similar geometries to those observed in the nature. This leads to consider the application of mathematical algorithms that solve the complex differential equations that govern the elastic behavior of rocks Still, when this type of technique is useful to obtain results that are compared favorably with the experimental observations, they introduce non-unique solutions, because different populations of pores that have been scaled from an original population can produce the same porosities and elastic responses. To solve this problem, we propose to make use of the concept of fractal geometry, in which the populations of pores inside the rock should follow a distribution of fractal type, which establishes unique relationships between the number of pores and their size. The fractal relation imposed on the model is similar to the one observed experimentally, as reported by several investigators in sedimentary rocks (sandstones, carbonates and shales). This way, it is possible to reduce the ambiguities of the proposed model. This method has been applied to generate a porosity and compressibility model of the Fountainebleau A sandstone.

Año de publicación:

1998

Keywords:

Fuente:

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scopus